Over medium is the yolk that’s slightly cooked—think jammy, not gushy. It’s the Goldilocks of eggs: not too runny, not too firm. You flip it and let it linger on the heat just a little longer while you count to twenty.
Over hard is for people who really hate mess. You break the yolk with your spatula and cook it until it’s solid and safe. Some call it overcooked; I call it “egg that won’t drip on your shirt during a job interview.”